<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <title>Title</title>
    <script src="../../js/jquery-3.4.1.js"></script>
    <script src="customize/jquery.date-util.js"></script>
</head>
<body>
<input type="text" id="startDate" />
<input type="text" id="endDate" />
<script type="text/javascript">

    Date.prototype.format = function (format) {
        var o = {
            "M+": this.getMonth() + 1, // month
            "d+": this.getDate(),    // day
            "h+": this.getHours(),   // hour
            "m+": this.getMinutes(), // minute
            "s+": this.getSeconds(), // second
            "q+": Math.floor((this.getMonth() + 3) / 3),  // quarter
            "S": this.getMilliseconds() // millisecond
        };
        if (/(y+)/.test(format))
            format = format.replace(RegExp.$1, (this.getFullYear() + "").substr(4 - RegExp.$1.length));
        for (var k in o)
            if (new RegExp("(" + k + ")").test(format))
                format = format.replace(RegExp.$1, RegExp.$1.length == 1 ? o[k] : ("00" + o[k]).substr(("" + o[k]).length));
        return format;
    };

    var date = new Date();

    var monthBeginDay = $.beginOfDay($.beginOfMonth(date)).format("yyyy-MM-dd hh:mm:ss");
    var monthEndDay = $.endOfDay($.endOfMonth(date)).format("yyyy-MM-dd hh:mm:ss");

    $('#startDate').val(monthBeginDay);
    $('#endDate').val(monthEndDay);

</script>
</body>
</html>